# How do you find the equation of exponential decay?

##### 1 Answer

Dec 9, 2014

Exponential decay and growth occurs widely in nature so I will use radioactive decay as an example.

When an atom decays it is a random, chance event. The number of atoms decaying per second depends only on the number of undecayed atoms N.

So we can write:

Rate of decay:

We can replace the

Rearranging gives:

Integrating both sides:

So

If we apply the limits of integration such that when

So

So

So